Polynomials over a fixed ring. More...

#include <polynomi.h>

Inheritance diagram for PolynomialOverFixedRing< T, instance >:

Public Types
typedef T	Ring

typedef T::Element	CoefficientType

typedef B::DivideByZero	DivideByZero

typedef B::RandomizationParameter	RandomizationParameter

Public Member Functions
ACCESSORS
int	Degree () const
	the zero polynomial will return a degree of -1

unsigned int	CoefficientCount () const
	degree + 1

CoefficientType	GetCoefficient (unsigned int i) const
	return coefficient for x^i

CoefficientType	operator[] (unsigned int i) const
	return coefficient for x^i

MANIPULATORS
ThisType &	operator= (const ThisType &t)

ThisType &	operator+= (const ThisType &t)

ThisType &	operator-= (const ThisType &t)

ThisType &	operator*= (const ThisType &t)

ThisType &	operator/= (const ThisType &t)

ThisType &	operator%= (const ThisType &t)

ThisType &	operator<<= (unsigned int n)

ThisType &	operator>>= (unsigned int n)

void	SetCoefficient (unsigned int i, const CoefficientType &value)
	set the coefficient for x^i to value

void	Randomize (RandomNumberGenerator &rng, const RandomizationParameter &parameter)

void	Negate ()

void	swap (ThisType &t)

UNARY OPERATORS
bool	operator! () const

ThisType	operator+ () const

ThisType	operator- () const

Friends
BINARY OPERATORS
ThisType	operator>> (ThisType a, unsigned int n)

ThisType	operator<< (ThisType a, unsigned int n)

INPUT/OUTPUT
std::istream &	operator>> (std::istream &in, ThisType &a)

std::ostream &	operator<< (std::ostream &out, const ThisType &a)

CREATORS
	PolynomialOverFixedRing (unsigned int count=0)
	creates the zero polynomial

	PolynomialOverFixedRing (const ThisType &t)
	copy constructor

	PolynomialOverFixedRing (const B &t)

	PolynomialOverFixedRing (const CoefficientType &element)
	construct constant polynomial

template<typename Iterator >
	PolynomialOverFixedRing (Iterator first, Iterator last)
	construct polynomial with specified coefficients, starting from coefficient of x^0

	PolynomialOverFixedRing (const char *str)
	convert from string

	PolynomialOverFixedRing (const byte *encodedPoly, unsigned int byteCount)
	convert from big-endian byte array

	PolynomialOverFixedRing (const byte *BEREncodedPoly)
	convert from Basic Encoding Rules encoded byte array

	PolynomialOverFixedRing (BufferedTransformation &bt)
	convert from BER encoded byte array stored in a BufferedTransformation object

	PolynomialOverFixedRing (RandomNumberGenerator &rng, const RandomizationParameter &parameter)
	create a random PolynomialOverFixedRing

static const ThisType &	Zero ()

static const ThisType &	One ()

OTHER ARITHMETIC FUNCTIONS
ThisType	MultiplicativeInverse () const

bool	IsUnit () const

ThisType	Doubled () const

ThisType	Squared () const

CoefficientType	EvaluateAt (const CoefficientType &x) const

static void	Divide (ThisType &r, ThisType &q, const ThisType &a, const ThisType &d)
	calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))

Detailed Description

template<class T, int instance>
class PolynomialOverFixedRing< T, instance >

Polynomials over a fixed ring.

Having a fixed ring allows overloaded operators

Definition at line 163 of file polynomi.h.

Member Typedef Documentation

◆ Ring

template<class T , int instance>

typedef T PolynomialOverFixedRing< T, instance >::Ring

Definition at line 169 of file polynomi.h.

◆ CoefficientType

template<class T , int instance>

typedef T::Element PolynomialOverFixedRing< T, instance >::CoefficientType

Definition at line 170 of file polynomi.h.

◆ DivideByZero

template<class T , int instance>

typedef B::DivideByZero PolynomialOverFixedRing< T, instance >::DivideByZero

Definition at line 171 of file polynomi.h.

◆ RandomizationParameter

template<class T , int instance>

typedef B::RandomizationParameter PolynomialOverFixedRing< T, instance >::RandomizationParameter

Definition at line 172 of file polynomi.h.

Constructor & Destructor Documentation

◆ PolynomialOverFixedRing() [1/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing ( unsigned int count = 0 )

inline

creates the zero polynomial

Definition at line 177 of file polynomi.h.

◆ PolynomialOverFixedRing() [2/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing ( const ThisType & t )

inline

copy constructor

Definition at line 180 of file polynomi.h.

◆ PolynomialOverFixedRing() [3/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing ( const B & t )

inlineexplicit

Definition at line 182 of file polynomi.h.

◆ PolynomialOverFixedRing() [4/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing ( const CoefficientType & element )

inline

construct constant polynomial

Definition at line 185 of file polynomi.h.

◆ PolynomialOverFixedRing() [5/10]

template<class T , int instance>

template<typename Iterator >

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing	(	Iterator	first,
		Iterator	last )

inline

construct polynomial with specified coefficients, starting from coefficient of x^0

Definition at line 188 of file polynomi.h.

◆ PolynomialOverFixedRing() [6/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing ( const char * str )

inlineexplicit

convert from string

Definition at line 192 of file polynomi.h.

◆ PolynomialOverFixedRing() [7/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing	(	const byte *	encodedPoly,
		unsigned int	byteCount )

inline

convert from big-endian byte array

Definition at line 195 of file polynomi.h.

◆ PolynomialOverFixedRing() [8/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing ( const byte * BEREncodedPoly )

inlineexplicit

convert from Basic Encoding Rules encoded byte array

Definition at line 198 of file polynomi.h.

◆ PolynomialOverFixedRing() [9/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing ( BufferedTransformation & bt )

inlineexplicit

convert from BER encoded byte array stored in a BufferedTransformation object

Definition at line 201 of file polynomi.h.

◆ PolynomialOverFixedRing() [10/10]

template<class T , int instance>

PolynomialOverFixedRing< T, instance >::PolynomialOverFixedRing	(	RandomNumberGenerator &	rng,
		const RandomizationParameter &	parameter )

inline

create a random PolynomialOverFixedRing

Definition at line 204 of file polynomi.h.

Member Function Documentation

◆ Zero()

template<class T , int instance>

const PolynomialOverFixedRing< T, instance > & PolynomialOverFixedRing< T, instance >::Zero ( )

static

Definition at line 566 of file polynomi.cpp.

◆ One()

template<class T , int instance>

const PolynomialOverFixedRing< T, instance > & PolynomialOverFixedRing< T, instance >::One ( )

static

Definition at line 572 of file polynomi.cpp.

◆ Degree()

template<class T , int instance>

int PolynomialOverFixedRing< T, instance >::Degree ( ) const

inline

the zero polynomial will return a degree of -1

Definition at line 213 of file polynomi.h.

◆ CoefficientCount()

template<class T , int instance>

unsigned int PolynomialOverFixedRing< T, instance >::CoefficientCount ( ) const

inline

degree + 1

Definition at line 215 of file polynomi.h.

◆ GetCoefficient()

template<class T , int instance>

CoefficientType PolynomialOverFixedRing< T, instance >::GetCoefficient ( unsigned int i ) const

inline

return coefficient for x^i

Definition at line 217 of file polynomi.h.

◆ operator[]()

template<class T , int instance>

CoefficientType PolynomialOverFixedRing< T, instance >::operator[] ( unsigned int i ) const

inline

return coefficient for x^i

Definition at line 219 of file polynomi.h.

◆ operator=()

template<class T , int instance>

ThisType & PolynomialOverFixedRing< T, instance >::operator= ( const ThisType & t )

inline

Definition at line 225 of file polynomi.h.

◆ operator+=()

template<class T , int instance>

ThisType & PolynomialOverFixedRing< T, instance >::operator+= ( const ThisType & t )

inline

Definition at line 227 of file polynomi.h.

◆ operator-=()

template<class T , int instance>

ThisType & PolynomialOverFixedRing< T, instance >::operator-= ( const ThisType & t )

inline

Definition at line 229 of file polynomi.h.

◆ operator*=()

template<class T , int instance>

ThisType & PolynomialOverFixedRing< T, instance >::operator*= ( const ThisType & t )

inline

Definition at line 231 of file polynomi.h.

◆ operator/=()

template<class T , int instance>

ThisType & PolynomialOverFixedRing< T, instance >::operator/= ( const ThisType & t )

inline

Definition at line 233 of file polynomi.h.

◆ operator%=()

template<class T , int instance>

ThisType & PolynomialOverFixedRing< T, instance >::operator%= ( const ThisType & t )

inline

Definition at line 235 of file polynomi.h.

◆ operator<<=()

template<class T , int instance>

ThisType & PolynomialOverFixedRing< T, instance >::operator<<= ( unsigned int n )

inline

Definition at line 238 of file polynomi.h.

◆ operator>>=()

template<class T , int instance>

ThisType & PolynomialOverFixedRing< T, instance >::operator>>= ( unsigned int n )

inline

Definition at line 240 of file polynomi.h.

◆ SetCoefficient()

template<class T , int instance>

void PolynomialOverFixedRing< T, instance >::SetCoefficient	(	unsigned int	i,
		const CoefficientType &	value )

inline

set the coefficient for x^i to value

Definition at line 243 of file polynomi.h.

◆ Randomize()

template<class T , int instance>

void PolynomialOverFixedRing< T, instance >::Randomize	(	RandomNumberGenerator &	rng,
		const RandomizationParameter &	parameter )

inline

Definition at line 246 of file polynomi.h.

◆ Negate()

template<class T , int instance>

void PolynomialOverFixedRing< T, instance >::Negate ( )

inline

Definition at line 249 of file polynomi.h.

◆ swap()

template<class T , int instance>

void PolynomialOverFixedRing< T, instance >::swap ( ThisType & t )

inline

Definition at line 251 of file polynomi.h.

◆ operator!()

template<class T , int instance>

bool PolynomialOverFixedRing< T, instance >::operator! ( ) const

inline

Definition at line 257 of file polynomi.h.

◆ operator+()

template<class T , int instance>

ThisType PolynomialOverFixedRing< T, instance >::operator+ ( ) const

inline

Definition at line 259 of file polynomi.h.

◆ operator-()

template<class T , int instance>

ThisType PolynomialOverFixedRing< T, instance >::operator- ( ) const

inline

Definition at line 261 of file polynomi.h.

◆ MultiplicativeInverse()

template<class T , int instance>

ThisType PolynomialOverFixedRing< T, instance >::MultiplicativeInverse ( ) const

inline

Definition at line 275 of file polynomi.h.

◆ IsUnit()

template<class T , int instance>

bool PolynomialOverFixedRing< T, instance >::IsUnit ( ) const

inline

Definition at line 277 of file polynomi.h.

◆ Doubled()

template<class T , int instance>

ThisType PolynomialOverFixedRing< T, instance >::Doubled ( ) const

inline

Definition at line 280 of file polynomi.h.

◆ Squared()

template<class T , int instance>

ThisType PolynomialOverFixedRing< T, instance >::Squared ( ) const

inline

Definition at line 282 of file polynomi.h.

◆ EvaluateAt()

template<class T , int instance>

CoefficientType PolynomialOverFixedRing< T, instance >::EvaluateAt ( const CoefficientType & x ) const

inline

Definition at line 284 of file polynomi.h.

◆ Divide()

template<class T , int instance>

static void PolynomialOverFixedRing< T, instance >::Divide	(	ThisType &	r,
		ThisType &	q,
		const ThisType &	a,
		const ThisType &	d )

inlinestatic

calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))

Definition at line 287 of file polynomi.h.

Friends And Related Symbol Documentation

◆ operator>> [1/2]

template<class T , int instance>

ThisType operator>>	(	ThisType	a,
		unsigned int	n )

friend

Definition at line 267 of file polynomi.h.

◆ operator<< [1/2]

template<class T , int instance>

ThisType operator<<	(	ThisType	a,
		unsigned int	n )

friend

Definition at line 269 of file polynomi.h.

◆ operator>> [2/2]

template<class T , int instance>

std::istream & operator>>	(	std::istream &	in,
		ThisType &	a )

friend

Definition at line 294 of file polynomi.h.

◆ operator<< [2/2]

template<class T , int instance>

std::ostream & operator<<	(	std::ostream &	out,
		const ThisType &	a )

friend

Definition at line 297 of file polynomi.h.

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Friends

INPUT/OUTPUT

CREATORS

OTHER ARITHMETIC FUNCTIONS

Detailed Description

Member Typedef Documentation

◆ Ring

◆ CoefficientType

◆ DivideByZero

◆ RandomizationParameter

Constructor & Destructor Documentation

◆ PolynomialOverFixedRing() [1/10]

◆ PolynomialOverFixedRing() [2/10]

◆ PolynomialOverFixedRing() [3/10]

◆ PolynomialOverFixedRing() [4/10]

◆ PolynomialOverFixedRing() [5/10]

◆ PolynomialOverFixedRing() [6/10]

◆ PolynomialOverFixedRing() [7/10]

◆ PolynomialOverFixedRing() [8/10]

◆ PolynomialOverFixedRing() [9/10]

◆ PolynomialOverFixedRing() [10/10]

Member Function Documentation

◆ Zero()

◆ One()

◆ Degree()

◆ CoefficientCount()

◆ GetCoefficient()

◆ operator[]()

◆ operator=()

◆ operator+=()

◆ operator-=()

◆ operator*=()

◆ operator/=()

◆ operator%=()

◆ operator<<=()

◆ operator>>=()

◆ SetCoefficient()

◆ Randomize()

◆ Negate()

◆ swap()

◆ operator!()

◆ operator+()

◆ operator-()

◆ MultiplicativeInverse()

◆ IsUnit()

◆ Doubled()

◆ Squared()

◆ EvaluateAt()

◆ Divide()

Friends And Related Symbol Documentation

◆ operator>> [1/2]

◆ operator<< [1/2]

◆ operator>> [2/2]

◆ operator<< [2/2]